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for similar figures, area goes as square of ratio of dimensions
for similar figures, area goes as square of ratio of dimensions
Let's denote the lengths of the altitudes of the two similar trapezoids as h₁ and h₂ respectively.
Given that the ratio of the areas is 1/9, we have:
Area₁ / Area₂ = (h₁ * (a+b)) / (h₂ * (c+d)) = (h₁ / h₂) * ((a+b) / (c+d)) = 1/9
Here, a and b represent the lengths of the parallel sides of the first trapezoid, while c and d represent the lengths of the parallel sides of the second trapezoid.
Now, we can solve for the ratio of the lengths of the altitudes (h₁ / h₂):
(h₁ / h₂) = 1/9 * ((c+d) / (a+b))
Therefore, the ratio of the lengths of the altitudes of the two similar trapezoids is 1/9 multiplied by ((c+d) / (a+b)).